Mental Models Theory

Like the abstract-rule theory, the mental models theory, or more simply the model theory, proposes that people have a modicum of rationality, but that this rationality can be hampered by processing limitations (e.g., limited working memory; Johnson-Laird, 1983, 1995a, b, 1999; Johnson-Laird & Byrne, 1991, 1993a, 1996). Unlike the abstract-rule theory, the model theory gives comprehension a central role in reasoning; people build models when they comprehend linguistic descriptions and then their reasoning relies on these models. Indeed, the distinction between these two theories is paralleled by a distinction in logic, between logics based on syntactic methods using proofs and semantic methods using models. Abstract-rule theorists developed their ideas from proof systems, whereas model theorists have developed their ideas from logical, semantic systems. The proponents of this theory do not maintain that people use truth tables when they reason, but rather they see truth tables as containing a kernel of psychological truth (Johnson-Laird & Byrne, 1993b, p. 324).

Stated simply, the model theory maintains that people reason by constructing a representation or model of the state of affairs described in the premises, based on the meanings of the premises and general knowledge. They then describe this model in a parsimonious manner to generate a conclusion, before validating the model. Validation is carried out by searching for alternative models or counterexamples that refute the conclusion drawn. If no such counterexamples are found then subjects view the inference as being valid (Johnson-Laird & Byrne, 1991, 1993a). The basic idea can be illustrated easily in simple spatial problems (see Byrne & Johnson-Laird, 1989; Erlich & Johnson-Laird, 1982; Mani & Johnson-Laird, 1982).

Consider the representation or model one might build from the following set of premises, given the instructions to imagine the state of affairs described in them:

The lamp is on the right of the pad The book is on the left of the pad The clock is in front of the book The vase is in front of the lamp

Spatially, these objects can be viewed as being arranged in the following manner:

book pad lamp clock vase

So, one could make the novel inference from this model that "the clock is to the left of the vase". A novel inference or conclusion is any statement that follows from the premises and was not explicitly stated in them (so, many more could be made). If we try to refute this conclusion then we need to discover another layout or model of the objects that is consistent with the description in the premises, but is not consistent with the conclusion of "the clock is on the left of the vase" (i.e., we need to find a counterexample). In fact, there is no such model. But consider the following premises:

The lamp is on the right of the pad The book is on the left of the lamp The clock is in front of the book The vase is in front of the pad

This is consistent with two distinct models (see Byrne & Johnson-Laird, 1989):

book pad lamp pad book lamp clock vase vase clock

In this case, the conclusion that we might make from the first model, that "the clock is to the left of the vase", is inconsistent with an alternative model of the premises in which "the clock is to the right of the vase" (i.e., a counterexample can be found). Thus, in this case, one would have to admit that "there is no valid conclusion" to be made about the relationship of the vase and the clock on their own.

Several variants of the model theory have been proposed, which represent models in distinct ways; like Euler circles (Erickson, 1974; Guyote & Sternberg, 1981) or Venn diagrams (Newell, 1981). We will concentrate on a more general scheme initially proposed by Johnson-Laird (1983) and extended by Johnson-Laird and Byrne (1991, 1993a) which is summarised in Panel 16.2. We have already seen, in a rough

PANEL 16.2:

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